Simplify ((7b^3c^4n)/(3bc^5n))^-3

${(\frac{7 b^{3} c^{4} n}{3 b c^{5} n})}^{- 3}$

Cancel the common factor of $b^{3}$ and $b$ .

Factor $b$ out of $7 b^{3} c^{4} n$ .

${(\frac{b (7 b^{2} c^{4} n)}{3 b c^{5} n})}^{- 3}$

Cancel the common factors.

Factor $b$ out of $3 b c^{5} n$ .

${(\frac{b (7 b^{2} c^{4} n)}{b (3 c^{5} n)})}^{- 3}$

Cancel the common factor.

${(\frac{b (7 b^{2} c^{4} n)}{b (3 c^{5} n)})}^{- 3}$

Rewrite the expression.

${(\frac{7 b^{2} c^{4} n}{3 c^{5} n})}^{- 3}$

Cancel the common factor of $c^{4}$ and $c^{5}$ .

Factor $c^{4}$ out of $7 b^{2} c^{4} n$ .

${(\frac{c^{4} (7 b^{2} n)}{3 c^{5} n})}^{- 3}$

Cancel the common factors.

Factor $c^{4}$ out of $3 c^{5} n$ .

${(\frac{c^{4} (7 b^{2} n)}{c^{4} (3 c n)})}^{- 3}$

Cancel the common factor.

${(\frac{c^{4} (7 b^{2} n)}{c^{4} (3 c n)})}^{- 3}$

Rewrite the expression.

${(\frac{7 b^{2} n}{3 c n})}^{- 3}$

Cancel the common factor of $n$ .

Cancel the common factor.

${(\frac{7 b^{2} n}{3 c n})}^{- 3}$

Rewrite the expression.

${(\frac{7 b^{2}}{3 c})}^{- 3}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{3 c}{7 b^{2}})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{3 c}{7 b^{2}}$ .

$\frac{{(3 c)}^{3}}{{(7 b^{2})}^{3}}$

Apply the product rule to $3 c$ .

$\frac{3^{3} c^{3}}{{(7 b^{2})}^{3}}$

Apply the product rule to $7 b^{2}$ .

$\frac{3^{3} c^{3}}{7^{3} {(b^{2})}^{3}}$

Raise $3$ to the power of $3$ .

$\frac{27 c^{3}}{7^{3} {(b^{2})}^{3}}$

Simplify the denominator.

Raise $7$ to the power of $3$ .

$\frac{27 c^{3}}{343 {(b^{2})}^{3}}$

Multiply the exponents in ${(b^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{27 c^{3}}{343 b^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{27 c^{3}}{343 b^{6}}$